$g(x)=x^5$ $g'(x)=$
Solution: $g$ is of the form $x^n$ and therefore we can apply the power rule: $\dfrac{d}{dx}[x^n]=n\cdot x^{n-1}$ $\begin{aligned} g'(x)&=\dfrac{d}{dx}[x^{{5}}] \\\\ &={5}x^{{5}-1} \\\\ &=5x^4 \end{aligned}$ In conclusion, $g'(x)=5x^4$